Metastable Vacua in Large-$N$ QCD${}_3$

Abstract

We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD${}_3$) with gauge group $SU(N)$, $N_f$ fundamental quark flavors, and a level-$k$ Chern-Simons term. This analysis can be reliably carried out in the large-$N$, fixed $N_f,k$ limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-$N$ expansion we find $N_f+1$ distinct, exactly degenerate vacuum superselection sectors with different patterns of flavor-symmetry breaking. The associated massless Nambu-Goldstone bosons are generically accompanied by topological Chern-Simons theories. This set of vacua contains many candidate phases previously proposed for QCD${}_3$. At subleading order in the large-$N$ expansion, the exact degeneracy between the different superselection sectors is lifted, leading to a multitude of metastable vacua. If we dial the quark masses, different metastable vacua can become the true vacuum of the theory, leading to a sequence of first-order phase transitions. This intricate large-$N$ dynamics can be captured by the previously proposed bosonic dual theories for QCD${}_3$, provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.

57 pages, 11 figures; v2: added references and comment at the end of introduction

References in corpus (20)

• Generalized Global Symmetries
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Walking, Weak first-order transitions, and Complex CFTs
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Bosonization and Mirror Symmetry
• Gauge theory for the cuprates near optimal doping
• Nonsupersymmetric dualities from mirror symmetry
• More Abelian Dualities in 2+1 Dimensions
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• 3d Abelian Gauge Theories at the Boundary
• Enhanced thermal Hall effect in the square-lattice Néel state
• Bosonizing three-dimensional quiver gauge theories
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Exceptional Chern-Simons-Matter Dualities
• Bilinear condensate in three-dimensional large-$N_c$ QCD
• Charting the phase diagram of QCD${}_3$
• Random matrix approach to three-dimensional QCD with a Chern-Simons term

Cited by in corpus (13)

• Thermal Order in Conformal Theories
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• From 3d dualities to hadron physics
• Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Vacuum structure of large $N$ QCD${}_3$ from holography
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Holographic ${\mathrm{QCD}}_3$ and Chern-Simons theory from anisotropic supergravity
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities
• Cascade of phase transitions in a planar Dirac material
• Dualities of 3D $\mathcal{N}=1$ SQCD from Branes and non-SUSY deformations